A tolerance index based non-cooperative behaviour managing method with minimum cost in social network group decision making

This paper introduces a novel consensus theoretical framework designed to effectively manage non-cooperative behavior in social network group decision making (SNGDM). It addresses the challenge by considering both individuals' willingness to adjust preferences and the associated costs of achieving consensus. To deal with this issue, the personalized individual semantics (PIS) model is employed to handle original evaluation matrices by converting linguistic terms into numerical values based on experts' personalized opinions. Subsequently, a tolerance index (TI) is defined to reflect the willingness of experts to adjust their preferences. An improved minimum cost (MC) feedback model based on TI is established. The novelty of the proposed approach is that its integration of individual preference adjustment willingness and consensus efficiency, effectively preventing groupthink. In addition, a maximum group consensus degree optimisation model is proposed to detect non-cooperative behaviour of experts. To ensure an optimal solution for the minimum cost feedback model, a weight update method is proposed, considering the trust relationship between experts. A detailed analysis regarding the selection of tolerance thresholds to prevent over-penalisation of weights of non-collaborators is reported. Finally, comprehensive numerical and comparative analyses are presented to validate the proposed method.